A Short Proof of Fermats Last Theorem

Presented herein is a proof of Fermat’s Last Theorem, which is not only short (relative to Wiles’ 109 page proof), but is also performed using relatively elementary mathematics. Particularly, the binomial theorem is utilized, which was known in the time of Fermat (as opposed to the elliptic curves of Wiles’ proof, which belong to modern mathematics). Using the common integer expression n n n c b a = + for Fermat’s Last Theorem, the substitutions i a c + = and j b c + = are made, where i and j are integers. Using a Taylor expansion (i.e., in the form of the binomial theorem), Fermat’s Last Theorem reduces to the theorem that 1 − n n only has rational solutions for n=1 and n=2. This proof is presented herein, thus proving that n n n c b a = + only has integer solutions for a, b and c for integer values of the exponent n=1 or n=2.